Question: Solve for $x$ and $y$ using elimination. ${-3x-3y = -36}$ ${-5x+4y = -15}$
Explanation: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $4$ and the bottom equation by $3$ ${-12x-12y = -144}$ $-15x+12y = -45$ Add the top and bottom equations together. $-27x = -189$ $\dfrac{-27x}{{-27}} = \dfrac{-189}{{-27}}$ ${x = 7}$ Now that you know ${x = 7}$ , plug it back into $\thinspace {-3x-3y = -36}\thinspace$ to find $y$ ${-3}{(7)}{ - 3y = -36}$ $-21-3y = -36$ $-21{+21} - 3y = -36{+21}$ $-3y = -15$ $\dfrac{-3y}{{-3}} = \dfrac{-15}{{-3}}$ ${y = 5}$ You can also plug ${x = 7}$ into $\thinspace {-5x+4y = -15}\thinspace$ and get the same answer for $y$ : ${-5}{(7)}{ + 4y = -15}$ ${y = 5}$